Answer:
P(4 non-work-related e-mails)=0.1933
P(7 or more non-work-related e-mails)=0.1442
P(3 or less non-work-related e-mails)=0.3771
Step-by-step explanation:
A Poisson distribution is useful to measure the probability of a number of events in a given period, in this problem, receiving a non-work-related e-mail would be the event and an hour would be the period of time.
Its probability mass function is , being k the number of events and λ how many sucesses (events) are per period of time (4.3 in this case)
First, we calculate what is the probability of receiving exactly 4 e-mails:
As k is a discrete variable, to know the joint probability of different number of events we add the probability of each value.
The probability of receiving 7 or more is the sum of P(7), P(8), ..., P(∞):
Last, the probability of receiving 3 or less is the sum of P(0), P(1), P(2) and P(3):